It is very well known that microbial activity, ultimately the driver of SOM decomposition, is influenced by climatic parameters.

The most basic version of the ICBM model can be modified by rescaling the decay kinetics with climate: \[ \frac{dY_{(t)}}{dt}=I_{(t)} - k_y \cdot \color{red}{r} \cdot Y \\ \frac{dY_{(t)}}{dt}= h \cdot k_y \cdot \color{red}{r} \cdot Y - k_o \cdot \color{red}{r} \cdot O \] This scaling can be introduced as a variable over time (\(r_{(t)}\)) or as an average constant value (\(\bar{r}\)) (of course introducing a scaling variable over time destroys the steady state assumption).

The scaling is a function of soil temperature and soil moisture: \(r_{(t)}= f(temp, moist)\) And it does literally what it says: it rescales the kinetics \(k_y\) and \(k_o\) for the effect of climate, for example an increas or decrease of the microbial activity due to temperature.

Such scaling is composed by at least the two components of temperature and moisture. In ICBM this is done with a linear assumption of the effects: \[r_{clim}= r_{temp} \cdot r_{moist}\] But there is no difficulty in adding more processes if we think they are affecting the kinetics (for example we might want to represent clay protection as an additional linear term here, of course constant in this case since clay content in soil is always constant.)

There are various possibilities to represent the effect of temperature on microbial activity. These functions are classifiable under the following three groups:

Also for moisture the functions are classifiable under three groups:

While soil temperature does not pose big problems (we usually need to estimate it based on air temperature but we can use it at any aggregation level), soil water content is usually not measured and without available proxyes, and needs to be simulated.

Such simulation involves simulating the soil water balance, where inputs is what rains and outputs is what evaporates or leaches.
In this case the time scale does matter because precipitations accumulate. For example the average monthly precipitations is very different from the soil water balance (or even just all the water inputs) of that month.

The scaling for temperature is relatively straightforward: 1. Estimate soil temperature from air temperature
2. Calculate the temperature scaling based on soil temperature

The scaling for soil moisture is more complicated since it involves estimating the soil water content.
For this we need to:

1. Estimate the losses of water from soil due to evapotranspiration
   1.1 Estimate P.E.T.
   1.2 Estimate the evapotranspiration due to crops
   1.3 Estimate the total amount of water that can be retained

2. Calculate the water balance based on daily data

After this we can directly estimate the climate scaling due to soil water content.